As shown before in equation (REF ), in order to generate and evaluate samples using an MCMC sampler we require a proposal density \(q(x, y)\)  and must be able to evaluate the posterior at the generated sample. The MH algorithm assures that the proposal is reversible (i.e. \(q(x, y) = q(y, x)\) ) due to its criteria of accepting samples with a probability given by the acceptance ratio (REF ). So, any proposal density can be used. The authors in [1]} construct a proposal that is based on applying the motion model to one target at a time, per each MH sampling step:
\(Q(X^{^{\prime }}_{t}, X_{t}) = P(X^{^{\prime }}_{it}|X_{it})\) 
